As the expected frequencies of Red, Yellow & Orange are below 3, these polymorphisms must be grouped together (also based on our understanding of Jellybaby genetics). However, in the Bush habitat no yellow babies were found; they must be omitted from the analysis.
Observed Frequencies
Observed Frequencies
Black
Green
Orange, Red & Yellow
Total
Black
Green
Orange & Red
Total
Woods 1
6.666667
6
7.333333333
20
Bush 1
3
2
15
20
Woods 2
6.666667
6
7.333333333
20
Bush 2
5
4
11
20
Woods 3
6.666667
6
7.333333333
20
Bush 3
4
6
10
20
Total
20
18
22
0
0
60
Total
12
12
36
60
Expected Frequencies
Expected Frequencies
Black
Green
Orange, Red & Yellow
Total
Black
Green
Orange & Red
Total
Woods 1
4
4
12
20
Bush 1
4
4
12
20
Woods 2
4
4
12
20
Bush 2
4
4
12
20
Woods 3
4
4
12
20
Bush 3
4
4
12
20
Total
12
12
36
60
Total
12
12
36
60
Ho - There will be no significant differences in the frequency of jellybaby polymorphisms in the Woodland Habitat
O - E
Black
Green
Orange, Red & Yellow
2.666667
2
-4.666666667
2.666667
2
-4.666666667
2.666667
2
-4.666666667
8.000001
6
-14
(O - E)2 (Woodland)
Black
Green
Orange, Red & Yellow
64.00002
36
196
(O - E)2 / E
Total
5.333335
3
5.444444444
13.77777911
D.O.F = 4 (3-1 x 3-1) p = 13.77777911
According to a table of P values, with 4 degrees of freedom 13.7778 is significant, with a p value between 0.05 and 0.001.
We can reject the null hypothesis; there is a significant difference in the frequency of jelly babies in the woodland habitat & a low probability (< 5%) that sampling error would produce these results.
Ho - There will be no significant differences in the frequency of jellybaby polymorphisms in the Bush Habitat
O - E
Black
Green
Orange, Red & Yellow
Total
Bush 1
-1
-2
3
0
Bush 2
1
0
-1
0
Bush 3
0
2
-2
0
Total
0
0
0
0
(O - E)2 (Bush)
Black
Green
Orange, Red & Yellow
0
0
0
(O - E)2 / E
0
A p value of 0 was obtained. This does not exceed the critical threshold. The null hypothesis must be accepted. There is no significant difference in the frequency of polymorphisms in the Bush habitat.
Ho - There will be no significant differences in the frequency of jellybaby polymorphisms between the Woodland & Bush Habitats
O-E
Black
Green
Orange, Red & Yellow
Wood (Total)
8.000001
6
-14
Bush (Total)
0
0
0
Total
8
6
-14
(O - E)2
Black
Green
Orange, Red & Yellow
64.00002
36
196
(O - E)2 / E
5.333335
3
5.444444444
13.77777911
A p value of 13.77777911 was obtained. There are 2 degrees of freedom, the table of chi sqared results sets a critical value of 10.60 for p<0.05. As results exceed this value we can reject the null hypothesis. A significant difference in the jellybaby polymorphisms was observed & it is very unlikly that the results obtained were due to sampling error.
1
Black Green Orange Red Yellow
6 7 1 1 5
2
Black Green Orange Red
3 2 9 6
3
Black Green Orange Red
5 4 4 7
4
Black Green Orange Red
4 6 7 3
5
Black Green Orange Red Yellow
9 3 1 4 3
6
Black Green Red Yellow
5 8 4 3
Chi-Squared Analysis
As the expected frequencies of Red, Yellow & Orange are below 3, these polymorphisms must be grouped together (also based on our understanding of Jellybaby genetics). However, in the Bush habitat no yellow babies were found; they must be omitted from the analysis.
Ho - There will be no significant differences in the frequency of jellybaby polymorphisms in the Woodland Habitat
p = 13.77777911
According to a table of P values, with 4 degrees of freedom 13.7778 is significant, with a p value between 0.05 and 0.001.
We can reject the null hypothesis; there is a significant difference in the frequency of jelly babies in the woodland habitat & a low probability (< 5%) that sampling error would produce these results.
Ho - There will be no significant differences in the frequency of jellybaby polymorphisms in the Bush Habitat
Ho - There will be no significant differences in the frequency of jellybaby polymorphisms between the Woodland & Bush Habitats
A p value of 13.77777911 was obtained. There are 2 degrees of freedom, the table of chi sqared results sets a critical value of 10.60 for p<0.05. As results exceed this value we can reject the null hypothesis. A significant difference in the jellybaby polymorphisms was observed & it is very unlikly that the results obtained were due to sampling error.